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Algebraic number fields. (English) Zbl 0819.11044

Parshin, A. N. (ed.) et al., Number theory II: Algebraic number theory. Transl. from the Russian. Berlin: Springer-Verlag. Encycl. Math. Sci. 62, 1-269 (1992).
This survey of classical algebraic number theory, including class field theory, Galois theory of local and global fields, Iwasawa’s theory, \(p\)- adic \(L\)-functions and Fröhlich’s theory is a translation of the Russian edition [Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 62 (1990; Zbl 0722.11001)] with removed innumerous printing errors of the original.
For the entire collection see [Zbl 0814.00007].

MSC:

11Rxx Algebraic number theory: global fields
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11R23 Iwasawa theory
11R37 Class field theory
11R52 Quaternion and other division algebras: arithmetic, zeta functions
11R32 Galois theory
11R54 Other algebras and orders, and their zeta and \(L\)-functions
11R47 Other analytic theory
11R29 Class numbers, class groups, discriminants
11S31 Class field theory; \(p\)-adic formal groups
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
20E18 Limits, profinite groups
11S20 Galois theory

Citations:

Zbl 0722.11001
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